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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generation of linear evolution operators
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by Naoki Tanaka PDF
Proc. Amer. Math. Soc. 128 (2000), 2007-2015 Request permission

Abstract:

This paper is devoted to the problem of generation of evolution operators associated with linear evolution equations in a general Banach space. The stability condition is proposed from the viewpoint of finite difference approximations. It is shown that linear evolution operators can be generated even if the stability condition given here is assumed instead of Kato’s stability condition.
References
  • Tosio Kato, Linear evolution equations of “hyperbolic” type, J. Fac. Sci. Univ. Tokyo Sect. I 17 (1970), 241–258. MR 279626
  • Tosio Kato, Abstract evolution equations, linear and quasilinear, revisited, Functional analysis and related topics, 1991 (Kyoto), Lecture Notes in Math., vol. 1540, Springer, Berlin, 1993, pp. 103–125. MR 1225814, DOI 10.1007/BFb0085477
  • Kazuo Kobayasi, On a theorem for linear evolution equations of hyperbolic type, J. Math. Soc. Japan 31 (1979), no. 4, 647–654. MR 544682, DOI 10.2969/jmsj/03140647
  • Kazuo Kobayasi and Nobuhiro Sanekata, A method of iterations for quasi-linear evolution equations in nonreflexive Banach spaces, Hiroshima Math. J. 19 (1989), no. 3, 521–540. MR 1035141
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Additional Information
  • Naoki Tanaka
  • Affiliation: Department of Mathematics, Faculty of Science, Okayama University, Okayama 700-8530, Japan
  • Email: tanaka@math.okayama-u.ac.jp
  • Received by editor(s): May 4, 1998
  • Received by editor(s) in revised form: August 24, 1998
  • Published electronically: November 24, 1999
  • Communicated by: Dale Alspach
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 128 (2000), 2007-2015
  • MSC (1991): Primary 47D06; Secondary 34G10
  • DOI: https://doi.org/10.1090/S0002-9939-99-05263-6
  • MathSciNet review: 1654080